As is well known in the art, the acoustic piano generates or produces musical tones (sounds) with the strings struck by the associated hammers in accordance with the key strikes (depressions) by the player. Tones are generated from an acoustic piano differently in volume and resonance depending on the intensity or the speed of the key depression. An acoustic piano is equipped with pedals for controlling the sustention and the softness of the tones to be produced. A grand piano, for example, has a damper pedal, a sostenuto pedal and a shifting pedal (una corda pedal). Each of these pedals is constituted by a pedal lever which swings on (rotates around) a fulcrum or pivot provided in the bottom front area of the piano according to a depressing manipulation by the player's foot.
The damper pedal (hereinafter, simply the “pedal”) among others is a pedal to control the dampers for damping the vibrations of the piano strings and is most frequently used during the piano playing. The dampers are provided in a one damper to one key correspondence (one or two or three strings per key depending on the note range), and in the regular operation stays in touch with the corresponding string or strings at its rest position where the corresponding key is not depressed, goes off from the string(s) in response to the depression of the key to allow the string(s) to vibrate being hit by the hammer, and touches on to the string(s) again in response to the release of the key to suppress the vibration of the string(s), i.e. to stop the tone generation. The dampers are linked to the pedal via several connecting members. Between the connecting members are provided some clearances to cause some dead zone or ineffective stroke range of the pedal swing. A small or shallow depression of the pedal will, accordingly, not be transferred to the dampers. However, if the pedal is depressed to a significant extent, the swing of the pedal will then be transferred to the dampers so that the dampers shall be lifted off the strings not to damp the vibrations of the strings even after the fingers are released from the keys, whereby the tones of all the depressed keys will remain sounding. In addition, all the strings in the piano including the strings which correspond to the non-depressed keys will vibrate by resonation and the harmonic partial tones for the depressed keys will be enhanced in the produced sounds. Thus, the manipulation of the damper pedal operates the dampers to give abundance of expressions to the produced piano sounds.
For example, when the pedal is slowly depressed and slowly released statically (not dynamically), the pedal receives a reaction force (a force exerted toward the direction of return to the rest position, i.e. a load felt by the player's foot) from the damper-related mechanism. More specifically, as the pedal is being depressed by the player, the depressing force will be being transferred to the dampers via the connecting members, and the reaction force to the pedal will increase accordingly due to the reactions from the elastic elements constituting the connecting members and the weights and the frictions (with the strings) of the dampers which are being partly lifted off the strings in the depression ranges A0 and A1 in FIG. 4. As the pedal is further depressed, the dampers come off the strings completely, and the increase rate of the reaction force from elastic elements included in the connecting links becomes smaller, which means that the increase rate of the reaction force against the pedal in the depression range A2 is smaller than that in the depression range A1. The range bridging the latter half of the range A1 and the beginning part of the range A2 is called a half-pedal range AH. It is known that an advanced piano player can delicately control the tone color and the resonance of the generated piano sounds by delicately vary the depression amount of the pedal in the half-pedal range AH. Depending on the manufacturers and the models of acoustic pianos, the structures of the damper-related mechanisms including the pedal, the connecting members and the dampers may be different, which in turn may cause differences in the widths of the range A0, A1, AH and A2 and the positions of the boundaries between the adjacent ranges. Further, the increase rates of the reaction force in the ranges A0 and A1 may also be different as seen in FIG. 8.
An example of a pedal device to simulate the above-mentioned operational feeling of an acoustic piano in an electronic keyboard musical instrument is shown in unexamined Japanese patent publication No. 2004-334008. The illustrated pedal device of an electronic keyboard musical instrument comprises two swingable levers provided in a vertically spaced-apart and vertically pushing relation, two springs, each provided between one of the levers and a fixed member for urging the lever toward its rest position. As the front end of the lower lever (i.e. the pedal lever) is depressed by a foot and the rear end swings upward by a predetermined amount, the rear end touches the upper lever, and when the upper lever is pushed up by a certain amount, it drives the next members constituting the damper-related mechanism. Within the range where only the lower lever swings, the lower lever receives a reaction force from the spring urging the lower lever. As the lower lever (pedal lever) is further depressed to swing further to push up the upper lever, the lower lever receives a reaction force from the spring urging the upper lever in addition to the reaction force from the spring urging the lower lever. Thus, the rate of increase of the reaction force exerted on the pedal (i.e. lower) lever will be varied stepwise in accordance with the amount of depression of the pedal lever.
However, according to the idea of the above-mentioned prior art pedal device of an electronic keyboard musical instrument, all the movable members driven by the pedal manipulation are levers. So, if the stepwise variation of the friction force is to be increased and the number of levers is to be increased, the size of the pedal device will be increased accordingly, and problems will arise with the space for accommodation, the cost of manufacture, the design of the device, etc. Further, in the above-mentioned prior art pedal device of an electronic keyboard musical instrument, the curve of the pedal depression and reaction force characteristic is a simple superposition of linear functions according to the combination of the springs, which cannot realize a reaction force characteristic exhibiting a smaller rate of increase on the middle way of depression. Thus, the prior art pedal device for an electronic keyboard musical instrument cannot exactly simulate the reaction force characteristic of an acoustic piano.